{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 用来加载中文\n",
    "import matplotlib\n",
    "matplotlib.rcParams['font.sans-serif'] = ['SimHei']\n",
    "matplotlib.rcParams['font.family'] = 'sans-serif'\n",
    "matplotlib.rcParams['axes.unicode_minus'] = False # 用来正常显示负号"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loadDataSet(filename):\n",
    "    '''加载文件，将feature存在X中，y存在Y中'''\n",
    "    X = []\n",
    "    Y = []\n",
    "    with open(filename, 'rb') as f:\n",
    "        for idx, line in enumerate(f):\n",
    "            line = line.decode('utf-8').strip()\n",
    "            if not line:\n",
    "                continue\n",
    "                \n",
    "            eles = line.split()\n",
    "            if idx == 0:\n",
    "                numFeature = len(eles)\n",
    "            \n",
    "            eles = list(map(float, eles)) # 将数据转换成float型\n",
    "            \n",
    "            X.append(eles[:-1])   # 除最后一列都是feature，append(list)\n",
    "            Y.append([eles[-1]])    # 最后一列是实际值,同上\n",
    "            \n",
    "        return np.array(X), np.array(Y)   # 将X,Y列表转化成矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下定义**模型函数**：$$ h_\\theta(x) = \\theta_0 + \\theta_1 x $$\n",
    "$ h_\\theta(x) $ 为模型函数，用来预测<br/>\n",
    "$ \\theta_0 $ 、$ \\theta_1 $ 为模型参数<br/>\n",
    "$ x $ 为实际特征值<br/>\n",
    "$ \\theta_0 + \\theta_1 x $ 可以看做是 $ \\theta_0\\times1 + \\theta_1\\times x^{(i)} , i = 1,2,...,m $，表示共有 $ m $ 个样本<br/> \n",
    "即 \n",
    "$$\n",
    "{\\begin{bmatrix} \n",
    "1 & x^{(1)} \\\\\n",
    "1 & x^{(2)} \\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "1 & x^{(m)} \\\\\n",
    "\\end{bmatrix}}\\cdot\n",
    "{\\begin{bmatrix} \n",
    "\\theta_0 \\\\\n",
    "\\theta_1 \\\\\n",
    "\\end{bmatrix}} = \n",
    "{\\begin{bmatrix} \n",
    "y^{(1)} \\\\\n",
    "y^{(2)} \\\\\n",
    "\\vdots \\\\\n",
    "y^{(m)} \\\\\n",
    "\\end{bmatrix}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def h(theta, X):\n",
    "    '''定义模型函数'''\n",
    "    return np.dot(X, theta)  # 此时的X为处理后的X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下定义**cost function（代价函数）**：$$ J(\\theta_0, \\theta_1) = \\frac{1}{2m} \\sum_{i=1}^{m}(h_{\\theta}(x^{(i)})-y^{(i)})^2 $$\n",
    "而 $ (h_{\\theta}(x^{(i)})-y^{(i)})^2 = (h_{\\theta}(x^{(i)})-y^{(i)})^T \\cdot (h_{\\theta}(x^{(i)})-y^{(i)}) $ <br/>\n",
    "即\n",
    "$$\n",
    "{\\begin{bmatrix} \n",
    "(\\hat{y}^{(1)}-y^{(1)}) & (\\hat{y}^{(2)}-y^{(2)}) & \\cdots & (\\hat{y}^{(m)}-y^{(m)}) \\\\\n",
    "\\end{bmatrix}}\n",
    "\\cdot\n",
    "{\\begin{bmatrix} \n",
    "(\\hat{y}^{(1)}-y^{(1)}) \\\\\n",
    "(\\hat{y}^{(2)}-y^{(2)}) \\\\\n",
    "\\vdots \\\\\n",
    "(\\hat{y}^{(m)}-y^{(m)}) \\\\\n",
    "\\end{bmatrix}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J(theta, X, Y):\n",
    "    '''定义代价函数'''\n",
    "    m = len(X)\n",
    "    return np.sum(np.dot((h(theta,X)-Y).T, (h(theta,X)-Y))/(2 * m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下定义**梯度下降（BGD）公式**： $$ \\theta_0 := \\theta_0 - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)}) $$\n",
    "$$ \\theta_1 := \\theta_1 - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)}) \\cdot x^{(i)} $$\n",
    "**注意同步更新**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bgd(alpha, maxloop, epsilon, X, Y):\n",
    "    '''定义梯度下降公式，其中alpha为学习率控制步长，maxloop为最大迭代次数，epsilon为阈值控制迭代（判断收敛）'''\n",
    "    m, n = X.shape # m为样本数，n为特征数，在这里为2\n",
    "    \n",
    "    # 初始化参数为零\n",
    "    theta = np.zeros((2,1))\n",
    "    \n",
    "    count = 0 # 记录迭代次数\n",
    "    converged = False # 是否收敛标志\n",
    "    cost = np.inf # 初始化代价为无穷大\n",
    "    costs = [] # 记录每一次迭代的代价值\n",
    "    thetas = {0:[theta[0,0]], 1:[theta[1,0]]} # 记录每一轮theta的更新\n",
    "    \n",
    "    while count<= maxloop:\n",
    "        if converged:\n",
    "            break\n",
    "        # 更新theta\n",
    "        count = count + 1\n",
    "        \n",
    "        # 单独计算\n",
    "        #theta0 = theta[0,0] - alpha / m * (h(theta, X) - Y).sum()\n",
    "        #theta1 = theta[1,0] - alpha / m * (np.dot(X[:,1][:,np.newaxis].T,(h(theta, X) - Y))).sum()   # 重点注意一下    \n",
    "        # 同步更新\n",
    "        #theta[0,0] = theta0\n",
    "        #theta[1,0] = theta1\n",
    "        #thetas[0].append(theta0)\n",
    "        #thetas[1].append(theta1)\n",
    "        \n",
    "        # 一起计算\n",
    "        theta = theta - alpha / (1.0 * m) * np.dot(X.T, (h(theta, X)-Y))\n",
    "        # X.T : n*m , h(theta, Y) : m*1 , np.dot(X.T, (h(theta, X)- Y)) : n*1\n",
    "        # 同步更新\n",
    "        thetas[0].append(theta[0])\n",
    "        thetas[1].append(theta[1])        \n",
    "        \n",
    "        # 更新当前cost\n",
    "        cost = J(theta, X, Y)\n",
    "        costs.append(cost)\n",
    "        \n",
    "        # 如果收敛，则不再迭代\n",
    "        if cost<epsilon:\n",
    "            converged = True\n",
    "    return theta, costs, thetas "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. 下面进行回归测试：**<br/>\n",
    "（1）进行数据的读取与预处理：<br/>\n",
    "$ X_{m\\times1} $ --> $ X_{m\\times2} $<br>\n",
    "$ Y_{m\\times1} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(97, 1)\n",
      "(97, 1)\n"
     ]
    }
   ],
   "source": [
    "X, Y = loadDataSet('./data/ex1.txt')\n",
    "print(X.shape)\n",
    "print(Y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(97, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, n = X.shape\n",
    "X = np.concatenate((np.ones((m,1)), X), axis=1)   # 将第一列为1的矩阵，与原X相连\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）调用bgd函数，寻找最优参数（学习过程）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.02 # 学习率\n",
    "maxloop = 1500 # 最大迭代次数\n",
    "epsilon = 0.01 # 收敛判断条件\n",
    "\n",
    "resault = bgd(alpha, maxloop, epsilon, X, Y)\n",
    "theta, costs, thetas = resault  # 最优参数保存在theta中，costs保存每次迭代的代价值，thetas保存每次迭代更新的theta值\n",
    "#print(theta, costs[:5], thetas)\n",
    "# 到此，参数学习出来了，模型也就定下来了，若要预测新的实例，进行以下即可\n",
    "# Y_predict = h(theta, X_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. 以下为图形展示：**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(97,) (97, 1) (2, 1)\n"
     ]
    }
   ],
   "source": [
    "# 以下为训练集的预测值\n",
    "XCopy = X.copy()\n",
    "XCopy.sort(0)  # axis=0 表示列内排序\n",
    "yHat = h(theta, XCopy)\n",
    "print(XCopy[:,1].shape, yHat.shape, theta.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）绘制回归直线："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x257d6cf0da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制回归直线\n",
    "plt.xlabel(u'城市人口(万)')\n",
    "plt.ylabel(u'利润(万元)')\n",
    "plt.plot(XCopy[:,1], yHat,color='r')\n",
    "plt.scatter(X[:,1].flatten(), Y.T.flatten())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）绘制代价曲线："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.769642371667494 4.476999510945953\n"
     ]
    }
   ],
   "source": [
    "print(np.array(costs).max(),np.array(costs).min()) # 找到代价值的最大值、最小值，便于控制y轴范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x257d6cf09b0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x257d6cf09e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlim(-1,1600) # maxloop为1500\n",
    "plt.ylim(4,20)  \n",
    "plt.xlabel(u'迭代次数')\n",
    "plt.ylabel(u'代价函数J')\n",
    "plt.plot(range(len(costs)), costs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）绘制梯度下降过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.8782012979375224 0.11678270103092785\n"
     ]
    }
   ],
   "source": [
    "print(np.array(thetas[0]).min(), np.array(thetas[0]).max())  #查看theta0的范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 1.3065769949111339\n"
     ]
    }
   ],
   "source": [
    "print(np.array(thetas[1]).min(), np.array(thetas[1]).max())  #查看theta1的范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: Qt5Agg\n"
     ]
    }
   ],
   "source": [
    "# 准备网格数据，以备画梯度下降过程图\n",
    "%matplotlib\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "size = 100\n",
    "theta0Vals = np.linspace(-10,10, size)\n",
    "theta1Vals = np.linspace(-2, 4, size)\n",
    "JVals = np.zeros((size, size))   # 按照theta0Vals与theta1Vals 将JVals初始化为0\n",
    "for i in range(size):\n",
    "    for j in range(size):\n",
    "        col = np.matrix([[theta0Vals[i]], [theta1Vals[j]]])\n",
    "        JVals[i,j] = J(col, X, Y)\n",
    "\n",
    "theta0Vals, theta1Vals = np.meshgrid(theta0Vals, theta1Vals)\n",
    "JVals = JVals.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$J(\\\\theta)$')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 绘制3D代价函数图形\n",
    "contourSurf = plt.figure()\n",
    "ax = contourSurf.gca(projection='3d')\n",
    "\n",
    "ax.plot_surface(theta0Vals, theta1Vals, JVals,  rstride=2, cstride=2, alpha=0.3,\n",
    "                cmap=matplotlib.cm.rainbow, linewidth=0, antialiased=False)\n",
    "ax.plot(theta[0], theta[1], 'rx')\n",
    "ax.set_xlabel(r'$\\theta_0$')\n",
    "ax.set_ylabel(r'$\\theta_1$')\n",
    "ax.set_zlabel(r'$J(\\theta)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（4）绘制等高线图，查看下降过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1754ee21320>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1754b9ebf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制代价函数等高线图\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(12,6))\n",
    "CS = plt.contour(theta0Vals, theta1Vals, JVals, np.logspace(-2,3,30), alpha=.75)\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "\n",
    "# 绘制最优解\n",
    "plt.plot(theta[0,0], theta[1,0], 'rx', markersize=10, linewidth=3)\n",
    "\n",
    "# 绘制梯度下降过程\n",
    "plt.plot(thetas[0], thetas[1], 'rx', markersize=3, linewidth=1) # 每一次theta取值\n",
    "plt.plot(thetas[0], thetas[1], 'r-',markersize=3, linewidth=1) # 用线连起来"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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